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Physics 1A, Section 2 November 1, 2010 Slide 2 Office Hours Office hours will now be: Tuesday, 3:30 5:00 PM (half an hour later) still in Cahill 312 Slide 3 Todays Agenda Finish energy problem from Thursday forces and potential energy potential energy of a fictitious force? potential energy applied to orbits Lagrange points for Sun/Earth/satellite Slide 4 Quiz Problem 50 Slide 5 Answer: a)v = sqrt(2gh) b)F = -kx mg, to the right c)W = -kx s 2 /2 mgx s d)W f = 2 mgx s e)h = h 2 x s f)x s = [- mg + sqrt( 2 m 2 g 2 +2kmgh)]/k Slide 6 Conservative and Non-Conservative Forces A conservative force F can be associated with a potential energy U F = dU/dr or dU/dx in Physics 1a F = ( U/ x, U/ y, U/ z) more generally Force is a function of position only. example: uniform gravity: U = mgz example: Newtonian gravity: U = GMm/r example: ideal spring: U = kx 2 /2 Non-conservative forces friction: force depends on direction of motion normal force: depends on other forces but does no work because it has no component in direction of motion. Slide 7 Potential Energy from a Fictitious (Inertial) Force It can be useful to associate the centrifugal force in a rotating frame with a potential energy: F centrifugal = m 2 r (outward) Slide 8 Potential Energy from a Fictitious (Inertial) Force It can be useful to associate the centrifugal force in a rotating frame with a potential energy: F centrifugal = m 2 r (outward) U centrifugal = m 2 r 2 /2 Slide 9 Consider circular orbits (again) Work in the rotating (non-inertial) frame. planet orbiting the Sun: U total = U gravity + U centrifugal Equilibrium where dU total /dr = 0 GM Sun = 2 r 3 Slide 10 Consider circular orbits (again) Work in the rotating (non-inertial) frame. planet orbiting the Sun (M planet